Is there a way to animate objects as one temporarily without "independent movement"?
To animate a Rubik's cube:


Join all your cube in the same object with a ctrlJ.
Put the origin at the center of the object with a shiftctrlaltC > Origin to Geometry.
In Edit mode, select all and press P to Separate by Loose Parts. Now all the cubes are separate but they all have the same origin point. It will allow you to rotate them with the same rotation centre.
In Object mode, create an Empty at the same origin point, then select all your cubes and parent them to your Empty with a ctrlP > Object.
Put your timeline cursor at frame 0, select all your cubes and press i > LocRotScale. It will create the initial position of your Rubik's cube.
Make sure that your Pivot Point (on the horizontal menu bar on the bottom of the 3D View) is set on Median Point.
Put your timeline cursor at frame 10, select a face of your rubik's cube (i.e. 9 of your cubes) and rotate it on the X axis. Select all the cubes and Press i > LocRotScale.
Go on as many times as you want, it should work.